DESCARTES: undergraduate research
The DESCARTES Scholars Program is an NSF funded research and training program aimed at equipping applied math majors with advanced skills in mathematics and computational science. Applicants must be applied math majors in their first or second year (applications are now closed). I've been a graduate student mentor in the program since 2014 and have had the privilege of coaching five students continuously from their freshman year to graduation.
We've covered several different topics over the years, from basic numerical analysis to statistical learning. Students typically completed a summer project with poster and presentation at the end. Some examples of past projects can be found below.
Students explored the fractals created using Newton's Method. They wrote their own code and generated their own unique images. Example below.
Predicting Presidential Primary Votes
Students used raw primary election data, sanitized it, and trained simple neural networks to predict winners.
Analysis San Francisco Employment Data
Classification trees were trained to find important features in a data set of San Francisco Employment benefits
Analysis of Forbes 2000 Ranking
Several predicative methods were trained on the Forbes 2000 ranking of the worlds largest companies and compared using ROC curves.
Created Model Blockchain
Students created from scratch their own block-chain for recorded simulated transactions, complete with proof of work and encrypted signing.